It is a reasonable distance in Durham terms but not too far. Around 20 minutes as mentioned earlier. It's not too far away from the science site, just up a little to St Mary's then through the car park/along the front.
Some of your SGIA lectures might be at the science site anyway, though tutorials will usually be at AQ or around there (Southend House, Elvet House).
You probably won't notice the distance unless you have something immediately before or after a teaching session which is unlikely but does happen (see end of post).
The distance only bothered me when living at the top of Gilesgate and I needed to walk across there to hand in an essay. In my early days politics were on Old Elvet and were next door neighbours to Philosophy. The AQ building was only a year old and little was based there. Those were the days.
Durham offers quite a well balanced philosophical education at undergraduate level. The history and philosophy of science and medicine are some of the major research interests of staff, and their only specialist taught MA, but they also have expertise in metaphysics, moral philosophy/ethics, modern philosophy, political philosophy, logic and both Continental and Analytic Philosophy. It's a small department and not exactly a great number of modules on offer every year but there is a decent range in what is available. So although Durham don't offer the same number of modules larger departments do, I don't think they are as heavily foucused in just one or two areas as other universities and also don't spread themselves too thinly.
As a Phil Pol student you will have little opportunity to take any modules in history and philosophy of science and medicine as they offer only a relative handful of modules in this area. As you can see by looking at the faculty handbook, you have little choice in what you can do in first and second year. There are hist and phil of sci and med modules at level 1 but you are not able to take any as a joint honours student. In your third year you can chose modules in history of psychiatry, history of the body (actually a school of health module), science and religion, philosophical issues in the sciences and biomedical ethics. Biomedical ethics is, as the name suggests, a module focusing more on ethical issues in medicine and this is its primary focus but it still touches on history of medicine (in understanding the background and historical context of medical ethics, the Hippocratic Oath for example).
I took History and Theory of Medicine, History of Science and Philosophy of Science in my (second) first year. Histrory and PHilosophy were seperate modules then but they're combined now. I then took Biomedical Ethics in final year and a dissertation in History of Medicine in my final year
So I had no previous experience with history of science and medicine, and very little experience of philosophy of science, before I started my degree and it was only by chance that I ended up taking the level one modules. But I soon developed a real interest in it and hoping to study it at postgrad - though probably not at Durham as I fancy a change of scene after all these years.
So I wouldn't worry about it for two reasons; first is that you will only have an opportunity to study history and philosophy of medicine and science in your final year and, by then, you have probably developed your own interests and specialisms so, if you don't want to do them, there are other options. Second, I didn't have any experience myself but found I thoroughly enjoyed the modules and no prior experience or knowledge is required. If you want to know more about modules before doing them then you can always get opinions from current or previous students and also from academic staff.
In any normal department. In SGIA this isn't always guarenteed though. Philosophy will usually offer a range of tutorial slots, as will most module conveners in SGIA modules. But in one SGIA module in particular there were only two tutorial slots with the second immediately after the first. This isn't good if you have to miss a tutorial due to illness as it means you can't make it up at a later time.
I had a Modern Philosophy lecture immediately after a SGIA lecture in 2009-2010 (SGIA at 10, Philosophy at 11). Needless to say, I didn't attend a single MP lecture that year
(or any philosophy lecture, for that matter) but I was resitting the philosophy module as I didn't complete due to illness a few years earlier (though I knew the content so attending lectures was not needed). There were only one or two other people taking those modules and they all just left 10 minutes early, arriving about 2 to 5 minutes late for the lecture (which isn't a disaster and some lecturers might delay starting the lecture by a couple of minutes to allow people to arrive anyway).
But these clashes/near clashes should be rare in theory as philosophy and politics is a common JH degree so they will try their best to avoid timetable issues. In two "unrelated" courses, History of Art and Engineering for example, you'd expect more clashes.
*I'm aware there is no History of Art degree at Durham. I'm referring to the History of Art modules in the School of Education.